1,068 research outputs found
Heavy-traffic analysis of k-limited polling systems
In this paper we study a two-queue polling model with zero switch-over times
and -limited service (serve at most customers during one visit period
to queue , ) in each queue. The arrival processes at the two queues
are Poisson, and the service times are exponentially distributed. By increasing
the arrival intensities until one of the queues becomes critically loaded, we
derive exact heavy-traffic limits for the joint queue-length distribution using
a singular-perturbation technique. It turns out that the number of customers in
the stable queue has the same distribution as the number of customers in a
vacation system with Erlang- distributed vacations. The queue-length
distribution of the critically loaded queue, after applying an appropriate
scaling, is exponentially distributed. Finally, we show that the two
queue-length processes are independent in heavy traffic
Waiting times in a two-queue model with exhaustive and Bernoulli service
Network Analysis;operations research
Iterative approximation of k-limited polling systems
The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient
Stochastic bounds for order flow times in warehouses with remotely located order-picking workstations
This paper focuses on the mathematical analysis of order flow times in parts-to-picker warehouses with remotely located order-picking workstations. To this end, a polling system with a new type of arrival process and service discipline is introduced as a model for an order-picking workstation. Stochastic bounds are deduced for the cycle time, which corresponds to the order flow time. These bounds are shown to be adequate and aid in setting targets for the throughput of the storage area. The paper thus complements existing literature, which mainly focuses on optimizing the operations in the storage area. Keywords: warehousing, order-picking workstation, order flow time, polling system, cycle time, stochastic bound
Workloads and waiting times in single-server systems with multiple customer classes
One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions
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